The Hindu religion believes that living a good life ruled by the eightfold path, as described by the Buddha, will bring you closer to being enlightened. The eight steps on the path will relieve suffering only in that when you die, you will be closer to understanding the four great truths, and therefore, you will be closer to enlightenment and the end of the cycle of suffering.

I consulted a friend who is well-versed in both Hinduism and Buddhism who has this to say about your question:

Both the question being asked and the answer are confusing 2 different things. The question, "What are the eight steps to relieve suffering according to Hindus?" doesn't make sense, since the 8 fold path is from Buddhism, not Hinduism and the 8 fold path and 4 noble truths are not intended to help you prepare for your death to find enlightenment, but how to live your life now, day to day. The 8 "prongs" of Patanjali are aspects of yoga, but not directly related to Buddhism and the 4 noble truths are concerned with recognizing that suffering exists, what causes suffering, how we can free ourselves from that suffering and how to live our daily lives. I see now why you thought it didn't make sense. Hope that helps a little.

The eight steps to relieve suffering according to Hindus is actually known as the Eightfold path. The Eightfold path was created in response to the Four Noble Truths set in place by Siddhartha Gautama, Buddha. The Fourth installment of the Four Noble Truths was "The way to overcome desire is to follow the eightfold path."

Now the Eightfold path is as follows:

Right views, Right aspirations, Right speech, Right conduct, Right livelihood, Right effort, Right mindfulness, and Right contemplation.